Finite Group Databasebeta

← #14908580

Subgroups — #14908580

Order 2816.

628 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078193C211yesmaximal, characteristic
2C2×D11×#107C211yesmaximal, characteristic, complemented
3#13070817C212yesmaximal, complemented
4#13070812C212yesmaximal, complemented
5#13070800C212yesmaximal, complemented
6#13070795C212yesmaximal, complemented
7#13070404C211yesmaximal, characteristic, complemented
8#13070402C211yesmaximal, characteristic, complemented
9#13070328C211yesmaximal, characteristic, complemented
10#13070226C211yesmaximal, characteristic, complemented
11C11×#2139C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13#10623359—21no—
14C22×C8×D11C2211yescharacteristic
15C2×C4⋊C4×D11—21no—
16C2×C11×M32C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18#10622846—21no—
19#10622801C2211yescharacteristic
20#10622801C2211yescharacteristic
21#10622784—21no—
22#10622784—21no—
23#10622770C2211yescharacteristic
24#10622770C2211yescharacteristic
25#10622719C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×#66876C2211yescharacteristic
28C2×#66871—21no—
29D11×#107—21no—
30D11×#107—21no—
31D11×#107C2212yes—
32D11×#107C2212yes—
33C11×#358C2212yescomplemented
34C11×#357C2212yescomplemented
35#10622202C2212yescomplemented
36#10622200C2212yescomplemented
37(C2×D11)⋊C16C2212yes—
38(C2×D11)⋊C16C2212yes—
39#10622143C2212yescomplemented
40#10622142C2212yescomplemented
41#10622128C2212yescomplemented
42#10622127C2212yescomplemented
43C2×C11×#41—21no—
44C22×C4×D11—41no—
45C22×C4×D11D411yescharacteristic
46C11×#135—22no—
47C11×#135—22no—
48C2×C11×Q16C2311yescharacteristic
49C2×C11×SD16—21no—
50C2×C11×D8C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C2×C11×C4⋊C4—21no—
53#66999—21no—
54#66999—21no—
55#66991—21no—
56#66991—21no—
57#66990—41no—
58#66988—41no—
59C4×C22⋊D11—41no—
60C4×C22⋊D11—41no—
61#66979—21no—
62C2×C4⋊Dic11—21no—
63C2×Dic11⋊C4—41no—
64C22×C11⋊C8D411yescharacteristic
65C2×C8×D11—22no—
66C2×C8×D11—22no—
67C2×C8×D11D411yescharacteristic
68C2×C8×D11D411yescharacteristic
69C2×C8×D11C2311yescharacteristic
70C2×C8×D11C2311yescharacteristic
71C4⋊C4×D11—22no—
72C4⋊C4×D11—22no—
73C4⋊C4×D11—41no—
74C4⋊C4×D11—41no—
75C11×M32—22no—
76C2×C11×C16C2312yes—
77C11×#107—21no—
78C11×#107C2312yes—
79#66899—21no—
80#66899—21no—
81#66896—21no—
82#66896—21no—
83#66882—21no—
84#66882C2312yes—
85#66882C2311yescharacteristic
86#66882C2311yescharacteristic
87#66881—21no—
88#66876—22no—
89C2×C11⋊C16C2312yes—
90#66871—22no—
91#66871—22no—
92#33646—111nomaximal, Sylow
93C23×D11D811yescharacteristic
94C11×#41—42no—
95C11×#41—42no—
96C2×Q8×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11C2×D411yescharacteristic
102C2×C22⋊D11—41no—
103C2×C22⋊D11—41no—
104C22×Dic11—41no—
105C22×Dic11D811yescharacteristic
106C2×C4×D11—22no—
107C2×C4×D11—22no—
108C2×C4×D11—42no—
109C2×C4×D11—42no—
110C2×C4×D11—84no—
111C2×C4×D11D811yescharacteristic
112C2×C4×D11D811yescharacteristic
113C2×C4×D11C2×D411yescharacteristic
114C2×C4×D11C2×D411yescharacteristic
115C11×Q16—21no—
116C11×Q16—21no—
117C11×SD16—42no—
118C11×D8—21no—
119C11×D8—21no—
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11#4112yes—
122C2×C8×C11#4112yes—
123C2×C8×C11C2411yescharacteristic
124C11×C4⋊C4—22no—
125C11×C4⋊C4—41no—
126C22⋊Dic11—41no—
127C22⋊Dic11—41no—
128C22⋊Dic11—41no—
129(C2×D11)⋊C4—41no—
130(C2×D11)⋊C4—41no—
131C4⋊Dic11—22no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134C4⋊Dic11—41no—
135Dic11⋊C4—42no—
136Dic11⋊C4—42no—
137Dic11⋊C4—41no—
138Dic11⋊C4—41no—
139C4×Dic11—41no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8C2×D411yescharacteristic
142C2×C11⋊C8C2×D411yescharacteristic
143C8×D11—22no—
144C8×D11—22no—
145C8×D11—21no—
146C8×D11—21no—
147C8×D11—21no—
148C8×D11—21no—
149C11×C16—22no—
150C11⋊C16—22no—
151#3050—111no—
152C22×#107—111no—
153#2236—112no—
154#2235—112no—
155#2233—112no—
156#2232—112no—
157#2159—111no—
158#2159—111no—
159#2139—111no—
160#2139D1111yescharacteristic, complemented
161#2112—111no—
162C23×C11—41no—
163C23×C11C2×D811yescharacteristic
164C22×D11—22no—
165C22×D11—22no—
166C22×D11—22no—
167C22×D11C2×D811yescharacteristic
168C22×D11C2×D811yescharacteristic
169Q8×C11—41no—
170Q8×C11—41no—
171D4×C11—41no—
172D4×C11—41no—
173D4×C11—82no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—82no—
177C2×C4×C11—82no—
178C2×C4×C11#12312yes—
179C2×C4×C11C2×D811yescharacteristic
180C2×C4×C11#13712yes—
181C2×C4×C11C22×D411yescharacteristic
182C22⋊D11—82no—
183C22⋊D11—82no—
184C2×Dic11—22no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—42no—
188C2×Dic11—82no—
189C2×Dic11C2×D811yescharacteristic
190C2×Dic11C2×D811yescharacteristic
191C4×D11—21no—
192C4×D11—21no—
193C4×D11—21no—
194C4×D11—21no—
195C4×D11—22no—
196C4×D11—22no—
197C4×D11—84no—
198C4×D11—84no—
199C8×C11#12312yes—
200C8×C11C2×#4111yescharacteristic
201C8×C11C2×#4111yescharacteristic
202C11⋊C8—21no—
203C11⋊C8—21no—
204C2×#135C2×D1111yescharacteristic
205C23×C8—111no—
206#525—221no—
207C22×C4⋊C4—221no—
208C2×M32—111no—
209C2×M32C2×D1111yescharacteristic
210#467—111no—
211#467—111no—
212#466—111no—
213#466—111no—
214#465—221no—
215#465—221no—
216#427—111no—
217C2×#107—111no—
218C2×#107—112no—
219C2×#107—112no—
220C2×#107—221no—
221C2×#107—221no—
222C2×#107—221no—
223C2×#107C2×D1111yescharacteristic
224#416—221no—
225#367—112no—
226#367—112no—
227#366—112no—
228#366—112no—
229#358—112no—
230#358C2×D1112yescomplemented
231#357—112no—
232#357C2×D1112yescomplemented
233C22⋊C16—112no—
234C22⋊C16—112no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—81no—
238C22×C11—81no—
239C22×C11—81no—
240C22×C11#48012yes—
241C22×C11C22×D811yescharacteristic
242C2×D11—28no—
243C2×D11—21no—
244C2×D11—21no—
245C2×D11—21no—
246C2×D11—21no—
247C2×D11#50912yes—
248C2×D11#51012yes—
249C4×C11—81no—
250C4×C11—82no—
251C4×C11#48012yes—
252C4×C11C2×#12311yescharacteristic
253C4×C11C2×#13711yescharacteristic
254Dic11—21no—
255Dic11—21no—
256Dic11—82no—
257Dic11—81no—
258Dic11—81no—
259C2×#41—21no—
260C23×C4—111no—
261C23×C4—441no—
262#135—22no—
263#135—22no—
264C2×Q16C22×D1111yescharacteristic
265C2×SD16—21no—
266C2×D8C22×D1111yescharacteristic
267C22×C8—111no—
268C22×C8—111no—
269C22×C8—111no—
270C22×C8—111no—
271C22×C8—111no—
272C22×C8—222no—
273C22×C8—222no—
274C22×C8C22×D1111yescharacteristic
275#123—441no—
276C22⋊Q8—221no—
277C22⋊Q8—221no—
278#121—221no—
279#121—221no—
280#120—441no—
281C4×D4—441no—
282C4×D4—441no—
283#117—221no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—222no—
286C2×C4⋊C4—222no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—441no—
289C2×C4⋊C4—441no—
290C2×C4⋊C4—441no—
291M32—22no—
292M32—222no—
293C2×C16—112no—
294C2×C16C22×D1112yes—
295#107—21no—
296#107—112no—
297#107—111no—
298#107—111no—
299#107—222no—
300#107—222no—
301#107—221no—
302#107C22×D1112yes—
303#106—221no—
304#103—221no—
305#103—221no—
306#102—221no—
307#102—221no—
308C2×C11—22no—
309C2×C11—161no—
310C2×C11C2×#48011yescharacteristic
311C2×C11C2×#50911yescharacteristic
312C2×C11C2×#51011yescharacteristic
313D11—22no—
314D11—22no—
315C24—111no—
316#41—42no—
317#41—42no—
318C2×Q8—21no—
319C2×D4—21no—
320C2×D4—41no—
321C2×D4—441no—
322C2×D4—441no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—111no—
326C22×C4—111no—
327C22×C4—111no—
328C22×C4—111no—
329C22×C4—111no—
330C22×C4—222no—
331C22×C4—222no—
332C22×C4—442no—
333C22×C4—442no—
334C22×C4—441no—
335C22×C4—884no—
336C22×C4D4×D1111yescharacteristic
337Q16—21no—
338Q16—21no—
339SD16—42no—
340D8—21no—
341D8—21no—
342C2×C8—111no—
343C2×C8—111no—
344C2×C8—222no—
345C2×C8—222no—
346C2×C8—222no—
347C2×C8—221no—
348C2×C8—221no—
349C2×C8—221no—
350C2×C8—221no—
351C2×C8#433912yes—
352C2×C8D4×D1111yescharacteristic
353C2×C8#434112yes—
354C2×C8C23×D1111yescharacteristic
355C4⋊C4—22no—
356C4⋊C4—41no—
357C4⋊C4—221no—
358C4⋊C4—221no—
359C4⋊C4—222no—
360C4⋊C4—442no—
361C4⋊C4—442no—
362C4⋊C4—441no—
363C4⋊C4—441no—
364C4⋊C4—441no—
365C22⋊C4—441no—
366C22⋊C4—441no—
367C22⋊C4—441no—
368C22⋊C4—441no—
369C22⋊C4—441no—
370C42—441no—
371C16—22no—
372C16—222no—
373C11#3364611yescharacteristic, complemented, Sylow
374C23—41no—
375C23—111no—
376C23—111no—
377C23—222no—
378C23—222no—
379C23—222no—
380C23D8×D1111yescharacteristic
381Q8—41no—
382Q8—41no—
383D4—41no—
384D4—41no—
385D4—82no—
386D4—882no—
387D4—882no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—111no—
393C2×C4—111no—
394C2×C4—222no—
395C2×C4—221no—
396C2×C4—221no—
397C2×C4—221no—
398C2×C4—221no—
399C2×C4—222no—
400C2×C4—222no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4—442no—
404C2×C4—884no—
405C2×C4—884no—
406C2×C4—882no—
407C2×C4#6693612yes—
408C2×C4D8×D1111yescharacteristic
409C2×C4#6696812yes—
410C2×C4C2×D4×D1111yescharacteristic
411C8—221no—
412C8—221no—
413C8#6693612yes—
414C8C2×#433911yescharacteristic
415C8C2×#434111yescharacteristic
416C22—21no—
417C22—21no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—112no—
422C22—112no—
423C22—228no—
424C22—221no—
425C22—221no—
426C22—221no—
427C22—221no—
428C22#1062238712yes—
429C22C2×D8×D1111yescharacteristic
430C4—82no—
431C4—81no—
432C4—221no—
433C4—221no—
434C4—882no—
435C4—881no—
436C4—881no—
437C4#1062238712yes—
438C4C2×#6693611yescharacteristic
439C4C2×#6696811yescharacteristic
440C2—22no—
441C2—161no—
442C2—222no—
443C2—222no—
444C2C2×#1062238711yescharacteristic
445C2D11×#50911yescharacteristic
446C2D11×#51011yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2139C2
socleC22×C11C22×D8
prime radical#13078193C2
hypercenter#2139D11
hypocenterC11#33646
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2139

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×D11×#107C2semidirect
3. #13070817C2semidirect
4. #13070812C2semidirect
5. #13070800C2semidirect
6. #13070795C2semidirect
7. #13070404C2semidirect
8. #13070402C2semidirect
9. #13070328C2semidirect
10. #13070226C2semidirect
11. C11×#2139C2semidirect
33. C11×#358C22semidirect
34. C11×#357C22semidirect
35. #10622202C22semidirect
36. #10622200C22semidirect
39. #10622143C22semidirect
40. #10622142C22semidirect
41. #10622128C22semidirect
42. #10622127C22semidirect
160. #2139D11semidirect
230. #358C2×D11semidirect
232. #357C2×D11semidirect
373. C11#33646semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130781932
C2×D11×#1072
#130708172
#130708122
#130708002
#130707952
#130704042
#130704022
#130703282
#130702262
C11×#21392
#3364611